The powers of a maximal ideal in a Banach algebra and analytic structure

Author:
T. T. Read

Journal:
Trans. Amer. Math. Soc. **161** (1971), 235-248

MSC:
Primary 46J20

DOI:
https://doi.org/10.1090/S0002-9947-1971-0435853-0

MathSciNet review:
0435853

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Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions are given for the existence of an analytic variety at an element of the spectrum of a commutative Banach algebra with identity. An associated graded algebra first considered by S. J. Sidney is used to determine the dimension of the analytic variety in terms of the closed powers of the maximal ideal which is the kernel of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0435853-0

Keywords:
Cmmutative Banach algebra with identity,
powers of a maximal ideal,
analytic structure,
dimension of an analytic variety,
graded algebra

Article copyright:
© Copyright 1971
American Mathematical Society